m is partly constant and partly varies as n square .when n equal to2,m equal to17,and when n equal to4,and equal to53.Find the equation connecting m and m.And find when m is equal to32
Yes
Yes
m = c + k n^2
17 = c + k *4
53 = c + k* 16
---------------------- subtract
-36 = -12 k
k = 3
then 17 = c + 4*3
c = 17 - 12 = 5
so m = 5 + 3 n
You can finish it.
To find the equation connecting m and n, we need to determine the relationship between the two variables.
We are given that m is partly constant and partly varies as n squared. This means that m can be expressed as the sum of a constant term and another term that is proportional to n squared.
Let's denote the constant term as a and the term proportional to n squared as bn^2. The equation connecting m and n can be written as:
m = a + bn^2
We are also given two specific values: when n = 2, m = 17, and when n = 4, m = 53. We can use these values to solve for a and b.
Substituting the first set of values into the equation, we have:
17 = a + b(2^2)
17 = a + 4b ---> Equation 1
Similarly, substituting the second set of values into the equation, we have:
53 = a + b(4^2)
53 = a + 16b ---> Equation 2
Now, we can solve these two equations simultaneously to find the values of a and b.
Subtracting Equation 1 from Equation 2, we get:
53 - 17 = (a + 16b) - (a + 4b)
36 = 12b
b = 3
Substituting this value of b back into Equation 1 or 2, we can solve for a:
17 = a + 4(3)
17 = a + 12
a = 5
Now we have the values of a and b, which allows us to write the equation connecting m and n:
m = 5 + 3n^2
To find when m is equal to 32, we substitute m = 32 into the equation:
32 = 5 + 3n^2
Rearranging the equation:
3n^2 = 32 - 5
3n^2 = 27
Dividing both sides by 3:
n^2 = 9
Taking the square root of both sides:
n = ±3
So, when m is equal to 32, n can be either 3 or -3.
Therefore, the equation connecting m and n is m = 5 + 3n^2, and when m = 32, n can be either 3 or -3.